David J. Heeger

The linear transform model of functional magnetic resonance imaging (fMRI) hypothesizes that fMRI responses are proportional to local average neural activity averaged over a period of time. This work reports results from three empirical tests that support this hypothesis. First, fMRI responses in human primary visual cortex (V1) depend separably on stimulus timing and stimulus contrast. Second, responses to long-duration stimuli can be predicted from responses to shorter duration stimuli. Third, the noise in the fMRI data is independent of stimulus contrast and temporal period. Although these tests can not prove the correctness of the linear transform model, they might have been used to reject the model. Because the linear transform model is consistent with our data, we proceeded to estimate the temporal fMRI impulse-response function and the underlying (presumably neural) contrast-response function of human V1.

Simple cells in the striate cortex have been depicted as half-wave-rectified linear operators. Complex cells have been depicted as energy mechanisms, constructed from the squared sum of the outputs of quadrature pairs of linear operators. However, the linear/energy model falls short of a complete explanation of striate cell responses. In this paper, a modified version of the linear/energy model is presented in which striate cells mutually inhibit one another, effectively normalizing their responses with respect to stimulus contrast. This paper reviews experimental measurements of striate cell responses, and shows that the new model explains a significantly larger body of physiological data.

One of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal and, in two dimensions, rotations of the input signal. The authors formalize these problems by defining a type of translation invariance called shiftability. In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be applied in the context of other domains, particularly orientation and scale. Jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored. Two examples of jointly shiftable transforms are designed and implemented: a 1-D transform that is jointly shiftable in position and scale, and a 2-D transform that is jointly shiftable in position and orientation. The usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>